1. Feed-forward neural networks
2. Recurrent neural networks
   1. SRN
   2. LSTM
   3. Bi-LSTM
   4. GRU

A machine learning subfield of learning representations of data. Exceptional effective at learning patterns.

Deep learning algorithms attempt to learn (multiple levels of) representation by using a hierarchy of multiple layers.

• A typical multi-layer network consists of an input, hidden and output layer, each fully connected to the next, with activation feeding forward.

• The weights determine the function computed.

objective/cost function \(J\)\((\theta)\)

Update each element of \(\theta\):

\[\theta^{new}_j = \theta^{old}_j - \alpha \frac{d}{\theta^{old}_j} J(\theta)\]

Matrix notation for all parameters ( \(\alpha\): learning rate):

\[\theta^{new}_j = \theta^{old}_j - \alpha \nabla _{\theta}J(\theta)\]

Recursively apply chain rule though each node

• Not guaranteed to converge to zero training error, may converge to local optima or oscillate indefinitely.
• However, in practice, does converge to low error for many large networks on real data.
• Many epochs (thousands) may be required, hours or days of training for large networks.
• To avoid local-minima problems, run several trials starting with different random weights (random restarts).
  • Take results of trial with lowest training set error.
  • Build a committee of results from multiple trials (possibly weighting votes by training set accuracy).

• Trained hidden units can be seen as newly constructed features that make the target concept linearly separable in the transformed space.
• On many real domains, hidden units can be interpreted as representing meaningful features such as vowel detectors or edge detectors, etc..
• However, the hidden layer can also become a distributed representation of the input in which each individual unit is not easily interpretable as a meaningful feature.

Learned hypothesis may fit the training data very well, even outliers ( noise) but fail to generalize to new examples (test data)

How to avoid overfitting?

• Running too many epochs can result in over-fitting.

• Keep a hold-out validation set and test accuracy on it after every epoch. Stop training when additional epochs actually increase validation error.
• To avoid losing training data for validation:
  • Use internal K-fold CV on the training set to compute the average number of epochs that maximizes generalization accuracy.
  • Train final network on complete training set for this many epochs.

• Use validation error to decide when to stop training
• Stop when monitored quantity has not improved after n subsequent epochs
• \(n\) is called patience

• Too few hidden units prevents the network from adequately fitting the data.
• Too many hidden units can result in over-fitting.

• Use internal cross-validation to empirically determine an optimal number of hidden units.

• Hyperparameter tuning

source: http://web.stanford.edu/class/cs224n/

• Add feedback loops where some units’ current outputs determine some future network inputs.
• RNNs can model dynamic finite-state machines, beyond the static combinatorial circuits modeled by feed-forward networks.

• Initially developed by Jeff Elman (“Finding structure in time,” 1990).
• Additional input to hidden layer is the state of the hidden layer in the previous time step.

• Behavior of RNN is perhaps best viewed by “unrolling” the network over time.

• RNNs can be trained using “backpropagation through time.”
• Can viewed as applying normal backprop to the unrolled network.

Suppose we had the following scenario:

Day 1: Lift Weights

Day 2: Swimming

Day 3: At this point, our model must decide whether we should take a rest day or yoga. Unfortunately, it only has access to the previous day. In other words, it knows we swam yesterday but it doesn’t know whether had taken a break the day before. Therefore, it can end up predicting yoga.

• Backpropagated errors multiply at each layer, resulting in exponential decay (if derivative is small) or growth (if derivative is large).
• Makes it very difficult train deep networks, or simple recurrent networks over many time steps.
• LSTMs were invented, to get around this problem.

https://towardsdatascience.com/

• LSTM networks, add additional gating units in each memory cell.
  • Forget gate
  • Input gate
  • Output gate
• Prevents vanishing/exploding gradient problem and allows network to retain state information over longer periods of time.

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–> –> –>

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–> –> –>

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–> –> –> –> –> –>

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–> –> –>

–> –> –> –> –> –> –> –>

• Separate LSTMs process sequence forward and backward and hidden layers at each time step are concatenated to form the cell output.

• Alternative RNN to LSTM that uses fewer gates (Cho, et al., 2014)
  • Combines forget and input gates into “update” gate.
  • Eliminates cell state vector

\[z_t = \sigma(W_z \cdot [h_{t-1}, x_t])\] \[r_t = \sigma(W_r \cdot [h_{t-1}, x_t])\] \[\tilde{h}_t = tanh(W \cdot [r_t * h_{t-1}, x_t])\] \[h_t = (1 - z_t) * h_{t-1} + z_t * \tilde(h)_t\]

• For many applications, it helps to add “attention” to RNNs.
• Allows network to learn to attend to different parts of the input at different time steps, shifting its attention to focus on different aspects during its processing.
• Used in image captioning to focus on different parts of an image when generating different parts of the output sentence.
• In MT, allows focusing attention on different parts of the source sentence when generating different parts of the translation.

• Deep learning can be applied for automatic feature engineering
• Recurrent neural networks are are ideal for sequential data such as text